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On Lindel¨of uniform frames and the axiom of countable choice
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: B. Banaschewski J.L. Walters-WaylandThis paper takes another look at the result that any complete separable uniform frame is Lindelöf and some of its ramifications. In particular, it shows that this is equivalent to the axiom of countable choice and provides a new, considerably... -
On characterization of a Riesz homomorphism on C(X)-space
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Z. Ercan S. ÖnalLet X be a realcompact space. We present a very simple and elementary proof of the well known fact that every Riesz homomorphism π: C(X) → R is point evaluated. Moreover, the proof is given in ZF. -
Hard pseudocompact spaces
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Partha Pratim Ghosh --- Indian Statistical Institute, North East Centre, India Biswajit Mitra --- School of Mathematical Sciences, South AfricaThe purpose of this paper is to show that hard pseudocompact spaces are indeed a significant generalisation of pseudocompact spaces on one hand and realcompact spaces on the other. To achieve this we have provided four intrinsic characterisations of hard... -
Connectedness modulo an ideal; a characterization theorem
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: M.R. Koushesh --- Isfahan University of Technology, IranLet X be a topological space and let be an ideal of subsets of X. The space X is called connected modulo if there is no continuous mapping f : X → [0, 1] which is 2-valued modulo in the...